Properties

Label 273.1.bm
Level $273$
Weight $1$
Character orbit 273.bm
Rep. character $\chi_{273}(191,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $37$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 273.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(37\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(273, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 6 6 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 4 0 0

Trace form

\( 6q + 2q^{3} - q^{4} - 2q^{6} + 3q^{7} - 2q^{9} + O(q^{10}) \) \( 6q + 2q^{3} - q^{4} - 2q^{6} + 3q^{7} - 2q^{9} - 4q^{10} - q^{12} - 5q^{13} - 2q^{15} + q^{16} - 2q^{19} - q^{21} + 4q^{24} - q^{25} + 2q^{27} + 2q^{28} + 4q^{34} - q^{36} - q^{37} - q^{39} + 2q^{40} - 2q^{42} - q^{43} - 2q^{46} - q^{48} + 3q^{49} + 2q^{51} - q^{52} + 2q^{54} - 2q^{57} + 4q^{58} - 2q^{61} - 5q^{63} - 2q^{64} + 4q^{67} + 2q^{69} - 4q^{70} - q^{73} - q^{75} + q^{76} + 2q^{78} - 4q^{79} + 6q^{81} - 4q^{82} + 2q^{84} - 2q^{85} + 2q^{87} + 4q^{90} - 2q^{91} - 2q^{93} - 4q^{94} + 3q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
273.1.bm.a \(2\) \(0.136\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-1\) \(q+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
273.1.bm.b \(4\) \(0.136\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots\)